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C₂×#13832 #513762

• p-group
• nilpotent
• supersolvable
• metabelian
• solvable
• monomial

Aliases

Subgroups

6842 conjugacy classes of subgroups.

Full subgroup data →

Presentation

A minimal faithful permutation representation — 5 generators on 26 points:

(1,2);(3,4,6,5)(7,8,10,9)(12,15)(13,17)(19,20,22,23)(21,24,25,26);(7,8,10,9)(12,15)(16,18)(20,23)(21,25);(3,5,6,4)(7,9,10,8)(11,12)(13,16)(14,15)(17,18)(19,21)(20,24)(22,25)(23,26);(11,13)(12,16)(14,17)(15,18)(19,20)(21,24)(22,23)(25,26)

Conjugacy classes & character table

152 conjugacy classes — view the full character table.

Relationships

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(512, 420958);